MENSURATION

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class 8 presentation on NCERT maths chapter -mensuration

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MENSURATION:

MENSURATION Guided by- Sri S K Nath sir

Contents:

Contents Introduction Trapezium Rhombus Cube Cuboid Cylinder Table Question Bank

Introduction:

Introduction Area of a trapezium =half of the sum of the length of parallel sides x perpendicular distance between them. a rhombus =half the product of its diagonals {d1 x d2} Surface area of a solid is the sum of the areas of its faces.

Introduction continued…:

Introduction continued… Surface area of a cuboid =2(lb +bh +hl) a cube =6l² a cylinder =2 π r (r+h) Volume –amount of region occupied by a solid is called its volume.

Introduction continued…:

Introduction continued… Volume of a cuboid=l x b x h a cube =l³ a cylinder= π r²h 1 cm³=1ml 1l=1000 cm² 1 m³=1000000 cm³=1000 l

TRAPEZIUM:

TRAPEZIUM A trapezium is a quadrilateral whose two sides are parallel. ABCD is a trapezium such that AB and CD are its two parallel sides while AD and BC are its non-parallel sides. Each of the two parallel sides of b trapezium is called base of the trapezium. The distance between the two bases (parallel sides) is called the height or altitude of the trapezium. Area of trapezium =half of the sum of the length of parallel sides x perpendicular distance between them. A D C B

Cube:

Cube A cube is b 3-D figure whose length , breadth and height are equal. It has six faces and all are squares and identical. Surface area of a cube = 6 x (length of the side)² Volume of a cube = (side)³

Rhombus:

Rhombus It is a quadrilateral whose all sides are equal out of which 2 opposite sides are parallel and none of the angles are right angles. Area of rhombus=½ x d1 x d2,where d1 and d2 are 2 diagonals

CUBOID:

CUBOID A cuboid is b 3-D figure which has six rectangular faces and opposite faces are identical. There are three pairs of identical faces. Surface area= 2x(lb + bh +lh) Volume= l x b x h

Cylinder :

Cylinder Cylinder is a 3–D figure which has one curved surface and two circular faces which are identical. Surface area of cylinder= 2 π r (r + h) Volume of cylinder= π r²h

Table:

Table Figure Volume Surface area Cuboid L x b x h 2(lb +bh +hl) Cube 6( l ) ² l ³ Cylinder π r²h 2 π r (r + h)

Question Bank Multiple-choice Questions:

Question Bank Multiple-choice Questions (i) Area of triangle (a) b x b (c) b x b (b) ½ x b x h (d) b x a Ans- ½ x b x h (ii) If the number of cement bags used to construct a path is needed, then the formulae to find the number of cement bags is - (a) area of path + area cemented by 1 bag

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(b) Area of the path x area of place cemented by 1 bag (c) Area of the path / area of the cemented place by 1 bag (d) none of these Ans- Area of the path / area of the cemented place by 1 bag (iii) What is the area of circle? (a) b x h (c) π r²

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(b) l x b (d) all of these Ans- π r² (iv) Area of the rhombus- (a) [area of triangle-1 + triangle-2] (b) length x breadth (c)½h(a+b) (d) diagonal 1 x diagonal 2 Ans- diagonal 1 x diagonal 2 (v) Volume of a cylinder is (a) l x b x h (b)l ³ (c) π r²h (d) None of these Ans- π r²h

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(vi) How many centimeters make a litre? (a)100 cm (b)1000 cm³ (c)both (b) and (a) (d) All of the above Ans- b)1000 cm³ (vii)How many pairs of faces in cuboids are identical? (a) 3 pairs (b) 6 pairs (c) 5 pairs (d) 10 pairs Ans- 3 pairs (vii) Perimeter of parallelogram (a) l x b (b) 2(l + b) (c) 4 x sides (d) None of these Ans- None of these

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(ix) Perimeter of circle (a) 2(l+b) (b) 3s (c) 2 π r (d) 4s Ans- 2 π r (x) Which are identical parts in cylinder (a) One curved surface and three circular faces (b) Two curved surface and one circular face (c) Both (a) and (b) (d) None of these Ans- None of these Correct answer-One curved surface and two circular faces

Short answer type questions:

Short answer type questions (1) What is triangulation? Ans- Splitting a quadrilateral into triangles, finding their areas and hence that of parallelogram (2) Find the area of a rhombus whose diagonals are of lengths 10 cm and 8.2cm . Ans- Area of rhombus= d1x d2 where d1,d2 are lengths of diagonals . =10 x 8.2 cm ² =41 cm² (3) Find the volume of the cube which has dimensions 2 x 2 x2 cm Ans- Volume of the cube = 6(l)² = 6(2)²=6 x 4 = 24 cm³ (4) In which unit is the volume expressed? Ans- cubic centimeter (cm³)

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(5)Find the area of quadrilateral PQRS shown in the figure. Ans- d=5.5 cm,h1=2.5 cm,h2=1.5 cm Area= ½ d(h1 + h2) =½ x 5.5 x (2.5+1.5)cm² =½ x 5.5 x 4 cm² =11 cm² P S R Q 1.5 5.5 2.5

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Presentation made by – Group : 3 Class : VIII-A Group members- Prangya Shree Tripathy Trupti Mayee Sahu Kalpana Behera Anwesha Panda

Thank you :

Thank you